Related papers: On the TAP free energy in the mixed $p$-spin model…
The Sherrington-Kirkpatrick Hamiltonian is a random quadratic function on the high-dimensional sphere. This article studies the ground state (i.e. maximum) of this Hamiltonian with external field, or more generally with a non-linear "spike"…
We prove the Thouless-Anderson-Palmer (TAP) equations for the local magnetization in the multi-species Sherrington-Kirkpatrick (MSK) spin glass model. One of the key ingredients is based on concentration results established…
We propose a simpler approach to identifying the limit of free energy in a vector spin glass model by adding a self-overlap correction to the Hamiltonian. This avoids constraining the self-overlap and allows us to identify the limit with…
We compute the complexity (logarithm of the number of TAP states) associated with minima and index-one saddle points of the TAP free energy. Higher-index saddles have smaller complexities. The two leading complexities are equal, consistent…
We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and…
In two papers Franz, Leone and Toninelli proved bounds for the free energy of diluted random constraints satisfaction problems, for a Poisson degree distribution [5] and a general distribution [6]. Panchenko and Talagrand [16] simplified…
We consider the problem of estimating the ground state energy of quantum $p$-local spin glass random Hamiltonians, the quantum analogues of widely studied classical spin glass models. Our main result shows that the maximum energy achievable…
The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd…
The expression of the free energy of a liquid in terms of an explicit decomposition of the particle configurations into local coordination clusters is examined. We argue that the major contribution to the entropy associated with structural…
This paper presents a meta-theory of the usage of the free energy principle (FEP) and examines its scope in the modelling of physical systems. We consider the so-called `map-territory fallacy' and the fallacious reification of model…
We conjecture an approximate expression for the free energy in the thermodynamic limit of the classical square lattice Ising model in a uniform (real) magnetic field. The zero-field result is well known due to Onsager for more than eighty…
We show that the limiting ground state energy of the spherical mixed p-spin model can be identified as the infimum of certain variational problem. This complements the well-known Parisi formula for the limiting free energy in the spherical…
We show that the thermodynamic limit of the ground state energy in the mixed p-spin model can be identified as a variational problem. This gives a natural generalization of the Parisi formula at zero temperature.
The free energy of multiple systems of spherical spin glasses with constrained overlaps was first studied in arXiv:math/0604082. The authors proved an upper bound of the constrained free energy using Guerra's interpolation. In this paper,…
We study the high-temperature regime of a mean-field spin glass model whose couplings matrix is orthogonally invariant in law. The magnetization of this model is conjectured to satisfy a system of TAP equations, originally derived by Parisi…
In this paper, we calculate the topological free energy for a number of ${\mathcal N} \geq 2$ Yang-Mills-Chern-Simons-matter theories at large $N$ and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the…
In the seminal work by G. Eilenberger [Z. Phys. 214, 195 (1968)], the quasiclassical expression for the free energy of spin-singlet superconductor has been suggested. Starting from the Luttinger-Ward formulation we derive the Eilenberger…
We revisit two classic Thouless-Anderson-Palmer (TAP) studies of the Sherrington-Kirkpatrick model [Bray A J and Moore M A 1980 J. Phys. C 13, L469; De Dominicis C and Young A P, 1983 J. Phys. A 16, 2063]. By using the…
We show that the formally exact expression for the free energy (with a non-relativistic Hamiltonian) for the correlated metal generates the Poisson equation within the saddle-point approximation for the electric potential, where the charge…
A quantum Parisi formula for the transverse field Sherrington-Kirkpatrick (SK) model is proven with an elementary mathematical method. First, a self-overlap corrected quantum model of the transverse field SK model is represented in terms of…